Finite Math Examples

$\begin{array}{c} x & P (x) \\ 2 & 0.5 \\ 3 & 0.5 \\ 4 & 0.7 \\ 1 & 0.8 \end{array}$

Step 1

A discrete random variable $x$ takes a set of separate values (such as $0$ , $1$ , $2$ ...). Its probability distribution assigns a probability $P (x)$ to each possible value $x$ . For each $x$ , the probability $P (x)$ falls between $0$ and $1$ inclusive and the sum of the probabilities for all the possible $x$ values equals to $1$ .

1. For each $x$ , $0 \leq P (x) \leq 1$ .

2. $P (x_{0}) + P (x_{1}) + P (x_{2}) + \dots + P (x_{n}) = 1$ .

Step 2

$0.5$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.5$ is between $0$ and $1$ inclusive

Step 3

$0.7$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.7$ is between $0$ and $1$ inclusive

Step 4

$0.8$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.8$ is between $0$ and $1$ inclusive

Step 5

For each $x$ , the probability $P (x)$ falls between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0 \leq P (x) \leq 1$ for all x values

Step 6

Find the sum of the probabilities for all the possible $x$ values.

$0.5 + 0.5 + 0.7 + 0.8$

Step 7

The sum of the probabilities for all the possible $x$ values is $0.5 + 0.5 + 0.7 + 0.8 = 2.5$ .

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Step 7.1

Add $0.5$ and $0.5$ .

$1 + 0.7 + 0.8$

Step 7.2

Add $1$ and $0.7$ .

$1.7 + 0.8$

Step 7.3

Add $1.7$ and $0.8$ .

$2.5$

Step 8

The sum of the probabilities for all the possible $x$ values is not equal to $1$ , which does not meet the second property of the probability distribution.

$0.5 + 0.5 + 0.7 + 0.8 = 2.5 \neq 1$

Step 9

For each $x$ , the probability $P (x)$ falls between $0$ and $1$ inclusive. However, the sum of the probabilities for all the possible $x$ values is not equal to $1$ , which means that the table does not satisfy the two properties of a probability distribution.

The table does not satisfy the two properties of a probability distribution